EECE 360/460 EECE 360/460 Matlab TutorialMatlab Tutorial

Jan 2011Jan 2011

OutlineOutline

What is Matlab?What is Matlab?Matlab InterfaceMatlab InterfaceBasic SyntaxBasic SyntaxPlotting Graphs Plotting Graphs Control System ToolboxControl System ToolboxExamplesExamplesUseful ResourcesUseful Resources

Overview of MatlabOverview of Matlab

What is Matlab?What is Matlab?

Language for technical computingLanguage for technical computing Supports mathematical computation, Supports mathematical computation,

visualization, and programmingvisualization, and programming Composed using high-level Composed using high-level

programming language programming language similar to syntax of Csimilar to syntax of C

For EECE 360 For EECE 360 Use Matlab in the assignmentsUse Matlab in the assignments

Matlab InterfaceMatlab Interface

Command Window

Workspace

CommandHistory

Change the current directory to the location of your

Matlab file at startup

Matlab ProgrammingMatlab Programming

Two ApproachesTwo ApproachesCoding in Command WindowCoding in Command Window

Good for short programsGood for short programsCommands must be re-entered each time you run Commands must be re-entered each time you run

a simulationa simulation

Coding with .m-filesCoding with .m-filesGood for long programsGood for long programsAllows users to save all the commands written in Allows users to save all the commands written in

the .m-filesthe .m-files

Command Window InterfaceCommand Window Interface

Write your commands here

(1) Creating .m-files

File New M-File

(2) Opening .m-filesFile Open select the .m-file

.m-file Interface.m-file Interface

Write your commands here

To run the program, press F5

Workspace InterfaceWorkspace Interface

The workspace provides a summary of the The workspace provides a summary of the variables variables

Command History InterfaceCommand History InterfaceThe Command History stores all the commands The Command History stores all the commands

entered in the entered in the Command WindowCommand Window previously previously No history of .m-files is shown hereNo history of .m-files is shown here

Syntax ErrorsSyntax Errors All errors are given in the All errors are given in the Command Window Command Window in in

redred Nature of error is explained Nature of error is explained

Examples on Examples on Matlab Interface Matlab Interface

Basic SyntaxBasic Syntax

Basic SyntaxBasic Syntax

Assignment of VariablesAssignment of VariablesSyntax: Syntax: Variable = ExpressionVariable = ExpressionExample: Example: A = 1;A = 1;

Use of semi-colonsUse of semi-colonsWith semi-colon – suppress outputWith semi-colon – suppress outputWithout semi-colon – displays output in Without semi-colon – displays output in

command windowcommand windowAdding commentsAdding comments

Add Add % % before command linebefore command lineExample:Example: % This is a demo % This is a demo

Basic Syntax (contBasic Syntax (cont’’d)d) Step incrementStep increment

Example: Example: k = 1:0.1:10k = 1:0.1:10 k is a row-matrix from 1 to 10 with step size = 0.1k is a row-matrix from 1 to 10 with step size = 0.1

Matrix ExpressionMatrix Expression

Hence, for a 2x2 matrix, the syntax isHence, for a 2x2 matrix, the syntax is A = [1 2; 3 4]A = [1 2; 3 4]

Row-matrixRow-matrix Column-matrixColumn-matrix

Basic Syntax (contBasic Syntax (cont’’d)d) Mathematical (Array) OperatorsMathematical (Array) Operators

Note the dimension of matrix in matrix computationNote the dimension of matrix in matrix computation Example: A: 2x1 matrix, B: 2x2 matrixExample: A: 2x1 matrix, B: 2x2 matrix

A*B A*B invalid operation invalid operation

B*A B*A valid operation valid operation

++ AdditionAddition

-- SubtractionSubtraction

** MultiplicationMultiplication

// DivisionDivision

^̂ PowerPower

Mathematical

++ AdditionAddition

-- SubtractionSubtraction

.*.* MultiplicationMultiplication

././ DivisionDivision

.^.^ PowerPower

Mathematical Array

Basic Syntax (contBasic Syntax (cont’’d)d)

Common Built-in Math FunctionsCommon Built-in Math Functions sin(x)sin(x) - sine - sine cos(x)cos(x) - cosine - cosine tan(x)tan(x) - tangent - tangent exp(x)exp(x) - exponential - exponential log10(x)log10(x) – base10 logarithm – base10 logarithm sqrt(x)sqrt(x) – square root – square root abs(x)abs(x) – absolute value – absolute value

The complete list can be found on pp. 833 of textThe complete list can be found on pp. 833 of text

Examples on Examples on Basic SyntaxBasic Syntax

Plotting GraphsPlotting Graphs

Plotting GraphsPlotting Graphs

Matlab allows graphical displays Matlab allows graphical displays By using the command By using the command plotplot Syntax: Syntax: plot(x)plot(x)

Types of plots Types of plots

Syntax: Syntax: plot(x,plot(x,’’--’’))

-- Solid lineSolid line

---- Dashed lineDashed line

:: Dotted lineDotted line

-.-. Dashdot lineDashdot line

Plotting Graphs (contPlotting Graphs (cont’’d)d)

Labeling GraphsLabeling GraphsCommonly used Syntax:Commonly used Syntax:

ylabel(ylabel(‘‘texttext’’)) – label y-axis – label y-axisxlabel(xlabel(‘‘texttext’’)) – label x-axis – label x-axistitle(title(‘‘texttext’’)) – label title – label titlelegend(legend(‘‘legend1legend1’’, , ‘‘length2length2’’,…),…) – puts legend on – puts legend on

current plotcurrent plotgrid on (grid off)grid on (grid off) – add (remove) grid lines to figure – add (remove) grid lines to figuresubplotsubplot – subdivides graphic window – subdivides graphic windowhold onhold on – hold the previous plot on the graphic – hold the previous plot on the graphic

windowwindow

Example (1)Example (1)

Example (2)Example (2)

subplot(2,2,1)plot(x,’r’),hold onplot(y,’--’)

subplot(2,2,2)plot(x,’r’),hold onplot(y,’--’)

subplot(2,2,3)plot(x,’r’),hold onplot(y,’--’)

subplot(2,2,4)plot(x,’r’),hold onplot(y,’--’)

Examples onExamples onPlotting GraphsPlotting Graphs

Control System ToolboxControl System Toolbox

Overview to the ToolboxOverview to the ToolboxModeled control systems asModeled control systems as

(1) transfer functions (1) transfer functions (2) zero-pole-gain (2) zero-pole-gain (3) state-space form(3) state-space form

Can manipulate both Can manipulate both (1) continuous-time system(1) continuous-time system(2) discrete-time system(2) discrete-time system

Can compute and graphCan compute and graph(1) time response (1) time response (2) frequency response(2) frequency response

Demo (1)Demo (1)Transfer FunctionTransfer Function

Syntax: Syntax: tf(numerator, denomintor)tf(numerator, denomintor)

Demo (2)Demo (2)

State-space RepresentationState-space Representation Syntax: Syntax: sys_ss = ss(sys)sys_ss = ss(sys)

Demo (3)Demo (3)

Finding Poles and ZerosFinding Poles and ZerosSyntax: Syntax: z = zero(sys)z = zero(sys)

p = pole(sys)p = pole(sys)

Pole-Zero DiagramPole-Zero DiagramSyntax: Syntax: zplane(z,p)zplane(z,p)

Demo (4)Demo (4) Closed-Loop SystemClosed-Loop System

Syntax: Syntax: CLsys = feedback(sys1,sys2)CLsys = feedback(sys1,sys2)

System 1

System 2

+

-

Demo (5) Demo (5)

Step ResponseStep ResponseSyntax: Syntax: step(sys)step(sys)

Demo (6)Demo (6)Pole-zero cancellationPole-zero cancellation

Syntax: Syntax: sysr = minreal(sys);sysr = minreal(sys); Impulse ResponseImpulse Response

Syntax: Syntax: impulse(sys)impulse(sys)

Examples onExamples onControl System ToolboxControl System Toolbox

Useful ResourcesUseful Resources

Appendix A of Textbook Appendix A of Textbook

End of Chapter – Matlab DemoEnd of Chapter – Matlab Demo

http://www.mathworks.comhttp://www.mathworks.com